Related papers: Generative models and Bayesian inversion using Lap…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning.…
Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable…
Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…
Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…
Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…
Model inversion attacks (MIAs) aim to reconstruct class-representative samples from trained models. Recent generative MIAs utilize generative adversarial networks to learn image priors that guide the inversion process, yielding…
Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in…